Elementary Number Theory – Helps solve this proof using the well command principle

Let $ a_1, a_2, …, a_n ∈ Bbb {N} $ . Prove that there is $ l ∈ Bbb {N} $ such as $ a_i | l $ for everyone $ i ∈ {1,2, …, n } $ and if $ x B Bbb {N} $ is such that each $ a_i $ Split $ x $then $ l | x $.

Hi, I know this proof includes a good command method method, maybe to find $ l $. But I am very confused as to how to solve it. Especially with the second half of the question. All answers are appreciated.